Siphon controllability definitions and issues

Deadlocks are an extremely undesirable situation in resource allocation systems. Nowadays, siphon control, which is based on siphon controllability conditions, is one of the important methods to ensure that deadlocks never occur in systems. For ordinary Petri nets, the siphon controllability condition is well defined. However, it remains an open question for generalized Petri nets despite many attempts to define their siphon controllability conditions. In recent years, many such conditions have been proposed for them or their subclasses, but suffer from various problems. This paper surveys the existing siphon controllability conditions and then presents two new ones. All of them are compared in terms of their condition strictness, application scope and equivalence. Future research directions are also indicated.